edu.jas.gb
Interface SolvableGroebnerBase<C extends RingElem<C>>

Type Parameters:

C - coefficient type

All Known Implementing Classes:

SolvableGroebnerBaseAbstract, SolvableGroebnerBaseParallel, SolvableGroebnerBaseSeq, SolvableGroebnerBaseSeqPairParallel

public interface SolvableGroebnerBase<C extends RingElem<C>>

Solvable Groebner Bases interface. Defines methods for left, right and twosided Groebner bases and left, right and twosided GB tests.

Author:

Heinz Kredel.

Method Summary

SolvableExtendedGB<C>	extLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) Solvable Extended Groebner base using critical pair class.
SolvableExtendedGB<C>	extLeftGB(java.util.List<GenSolvablePolynomial<C>> F) Solvable Extended Groebner base using critical pair class.
boolean	isLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) Left Groebner base test.
boolean	isLeftGB(java.util.List<GenSolvablePolynomial<C>> F) Left Groebner base test.
boolean	isLeftReductionMatrix(java.util.List<GenSolvablePolynomial<C>> F, java.util.List<GenSolvablePolynomial<C>> G, java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mf, java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mg) Test if left reduction matrix.
boolean	isLeftReductionMatrix(SolvableExtendedGB<C> exgb) Test if left reduction matrix.
boolean	isRightGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) Right Groebner base test.
boolean	isRightGB(java.util.List<GenSolvablePolynomial<C>> F) Right Groebner base test.
boolean	isTwosidedGB(int modv, java.util.List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base test.
boolean	isTwosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base test.
java.util.List<GenSolvablePolynomial<C>>	leftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) Left Groebner base using pairlist class.
java.util.List<GenSolvablePolynomial<C>>	leftGB(java.util.List<GenSolvablePolynomial<C>> F) Left Groebner base using pairlist class.
java.util.List<GenSolvablePolynomial<C>>	leftMinimalGB(java.util.List<GenSolvablePolynomial<C>> Gp) Left minimal ordered groebner basis.
java.util.List<GenSolvablePolynomial<C>>	rightGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) Right Groebner base using opposite ring left GB.
java.util.List<GenSolvablePolynomial<C>>	rightGB(java.util.List<GenSolvablePolynomial<C>> F) Right Groebner base using opposite ring left GB.
java.util.List<GenSolvablePolynomial<C>>	twosidedGB(int modv, java.util.List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base using pairlist class.
java.util.List<GenSolvablePolynomial<C>>	twosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base using pairlist class.

Method Detail

isLeftGB

boolean isLeftGB(java.util.List<GenSolvablePolynomial<C>> F)

Left Groebner base test.

Parameters:

F - solvable polynomial list.

Returns:

true, if F is a left Groebner base, else false.

isLeftGB

boolean isLeftGB(int modv,
                 java.util.List<GenSolvablePolynomial<C>> F)

Left Groebner base test.

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

true, if F is a left Groebner base, else false.

isTwosidedGB

boolean isTwosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp)

Twosided Groebner base test.

Parameters:

Fp - solvable polynomial list.

Returns:

true, if Fp is a two-sided Groebner base, else false.

isTwosidedGB

boolean isTwosidedGB(int modv,
                     java.util.List<GenSolvablePolynomial<C>> Fp)

Twosided Groebner base test.

Parameters:

modv - number of module variables.

Fp - solvable polynomial list.

Returns:

true, if Fp is a two-sided Groebner base, else false.

isRightGB

boolean isRightGB(java.util.List<GenSolvablePolynomial<C>> F)

Right Groebner base test.

Parameters:

F - solvable polynomial list.

Returns:

true, if F is a right Groebner base, else false.

isRightGB

boolean isRightGB(int modv,
                  java.util.List<GenSolvablePolynomial<C>> F)

Right Groebner base test.

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

true, if F is a right Groebner base, else false.

leftGB

java.util.List<GenSolvablePolynomial<C>> leftGB(java.util.List<GenSolvablePolynomial<C>> F)

Left Groebner base using pairlist class.

Parameters:

F - solvable polynomial list.

Returns:

leftGB(F) a left Groebner base of F.

leftGB

java.util.List<GenSolvablePolynomial<C>> leftGB(int modv,
                                                java.util.List<GenSolvablePolynomial<C>> F)

Left Groebner base using pairlist class.

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

leftGB(F) a left Groebner base of F.

extLeftGB

SolvableExtendedGB<C> extLeftGB(java.util.List<GenSolvablePolynomial<C>> F)

Solvable Extended Groebner base using critical pair class.

Parameters:

F - solvable polynomial list.

Returns:

a container for an extended left Groebner base of F.

extLeftGB

SolvableExtendedGB<C> extLeftGB(int modv,
                                java.util.List<GenSolvablePolynomial<C>> F)

Solvable Extended Groebner base using critical pair class.

Parameters:

modv - module variable number.

F - solvable polynomial list.

Returns:

a container for an extended left Groebner base of F.

leftMinimalGB

java.util.List<GenSolvablePolynomial<C>> leftMinimalGB(java.util.List<GenSolvablePolynomial<C>> Gp)

Left minimal ordered groebner basis.

Parameters:

Gp - a left Groebner base.

Returns:

leftGBmi(F) a minimal left Groebner base of Gp.

twosidedGB

java.util.List<GenSolvablePolynomial<C>> twosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp)

Twosided Groebner base using pairlist class.

Parameters:

Fp - solvable polynomial list.

Returns:

tsGB(Fp) a twosided Groebner base of Fp.

twosidedGB

java.util.List<GenSolvablePolynomial<C>> twosidedGB(int modv,
                                                    java.util.List<GenSolvablePolynomial<C>> Fp)

Twosided Groebner base using pairlist class.

Parameters:

modv - number of module variables.

Fp - solvable polynomial list.

Returns:

tsGB(Fp) a twosided Groebner base of Fp.

rightGB

java.util.List<GenSolvablePolynomial<C>> rightGB(java.util.List<GenSolvablePolynomial<C>> F)

Right Groebner base using opposite ring left GB.

Parameters:

F - solvable polynomial list.

Returns:

rightGB(F) a right Groebner base of F.

rightGB

java.util.List<GenSolvablePolynomial<C>> rightGB(int modv,
                                                 java.util.List<GenSolvablePolynomial<C>> F)

Right Groebner base using opposite ring left GB.

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

rightGB(F) a right Groebner base of F.

isLeftReductionMatrix

boolean isLeftReductionMatrix(SolvableExtendedGB<C> exgb)

Test if left reduction matrix.

Parameters:

exgb - an SolvableExtendedGB container.

Returns:

true, if exgb contains a left reduction matrix, else false.

isLeftReductionMatrix

boolean isLeftReductionMatrix(java.util.List<GenSolvablePolynomial<C>> F,
                              java.util.List<GenSolvablePolynomial<C>> G,
                              java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mf,
                              java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mg)

Test if left reduction matrix.

Parameters:

F - a solvable polynomial list.

G - a left Groebner base.

Mf - a possible left reduction matrix.

Mg - a possible left reduction matrix.

Returns:

true, if Mg and Mf are left reduction matrices, else false.